This may be naive, but would it be possible for the voltage booster to only start 'boosting' after the battery falls under a certain voltage threshold? That would be seem to solve both of your concerns.
The trouble is that the battery doesn't know the voltage requirements of the device it's powering. Should it start boosting at 1.4V? Or 1.25V? I have a hunch that it already does this for voltages near 1.5. The trouble is determining where you draw the line.
But they don't control the IP for the actual boost circuitry. Thats trivially easy to do. And from the comments in this thread it seems like lots of electronics already do it.
